Time Allocations, Social Norms, and Gender Gaps
Kazuharu Yanagimoto
December 16, 2022
Why is the gender wage gap large in Japan?
Why is the fraction of part-time workers large for women in Japan?
Choices on occupations and working hours
Utility cost associated to social norms
In Japanese statistics, a definition is used: Regular and Non-regular Jobs
However, they are typically
| Regular | Non-Regular | |
|---|---|---|
| Contract | Permanent | Temporary |
| Hours (week) | 40/40+ | Lower and Dispersed |
| Wage | High | Low |
In JPSED,
Goldin (2014) defines the two types of jobs by earning schedule
These characteristics correspond to Regular and Non-regular jobs!
Regression↗
If there are social norms regarding wives earning more than husbands, after the marriage, women might choose:
Using JPSED2016-2020, I see
Female earnings decline by 4496 EUR 1-year after the marriage
Other Outcomes↗
Sample: married, 25-59 aged in JPSED2016-2020
1. Participation Rate (0.27)
98 % (male) - 70 % (female)
2. Occupational Choices (0.59)
Fraction of regular workers. 89 % (male) - 32 % (female)
3. Labor Hours (0.49)
Mean of log working hours. 44.2 hours (male), 20.3 hours (female) per week
4. Wage (0.76)
Mean of log wage. 2958 JPY (male), 1534 JPY (female)
\[ \max_{h_m, h_f, T_m, T_f, j_m, j_f} U = \log c + \gamma \log H(1 - h_m - T_m, 1 - h_f - T_f) - \delta I\{e_m < e_f\} \]
subject to
\[\begin{aligned} c &= e(h_m, j_m) + e(h_f, j_f) \\ T &= T_m + T_f \end{aligned} \]
\(H(\cdot)\) : Joint leisure function
\(e(h, j)\) : Earning
\(T\) : Home hours requirement
\(\delta\) : Utility cost
Each husband and wife is endowed job specific productivity:
\[ \begin{pmatrix}a_{m, R} \\ a_{f, R} \\ a_{m, NR} \\ a_{f, NR}\end{pmatrix} \sim \log\mathcal{N}\left(\begin{pmatrix}0 \\ 0 \\ \mu_{NR} \\ \mu_{NR}\end{pmatrix}, \begin{pmatrix} \sigma^2 & \rho_{mf}\sigma^2 & \rho_{R, NR}\sigma^2 & \rho_{R, NR}\rho_{mf} \sigma^2 \\ \cdot & \sigma^2 & \rho_{R, NR}\rho_{mf} \sigma^2 & \rho_{R, NR} \sigma^2 \\ \cdot & \cdot & \sigma^2 & \rho_{mf} \sigma^2 \\ \cdot & \cdot & \cdot & \sigma^2 \end{pmatrix}\right) \]
\(\mu_{NR} < 0 \Rightarrow\) Non-regular workers earns less than regular worker
\(\rho_{mf} > 0 \Rightarrow\) Assortative Mating
\(\rho_{R, NR} > 0 \Rightarrow\) Regular and Non-regular abilities are linked
No Gender Difference in Productivity
Regular Jobs
\[ e(h, R) = \begin{cases} a_R h^{1 + \theta} & h < \bar{h} \\ a_R \left(\bar{h}^{1 + \theta} + \lambda_{R} \bar{h}^{\theta}(h - \bar{h})\right) & h > \bar{h} \end{cases} \]
Non-regular Jobs
\[ e(h, NR) = \begin{cases} a_{NR} h & h \le \bar{h} \\ a_{NR} \left(\bar{h} + \lambda_{NR} (h - \bar{h})\right) & h > \bar{h} \end{cases} \]
\[ H = \left(\nu(1 - h_m - T_m)^{\xi} + (1 - \nu)(1 - h_f - T_f)^{\xi}\right)^{1/\xi} \]
\(\nu\) : share parameter. Each household is endowed \(\nu \sim Beta(\alpha_{\nu}, \beta_{\nu})\)
\(\xi\) : complementarity. \(\xi < 0 \Rightarrow\) complement
\[ \begin{aligned} T &= T_m + T_f \\ \frac{1}{2}T & \sim Beta(\alpha_T, \beta_T) \end{aligned} \]
\[ \{\underbrace{\lambda_{R}, \lambda_{NR},\theta, }_{\text{production function}} \underbrace{\mu_{NR}, \sigma^2, \rho_{R, NR}, \rho_{mf},}_{\text{productivity}} \,\, \underbrace{\gamma, \xi, \alpha_{\nu}, \beta_{\nu},}_{\text{leisure}} \underbrace{\alpha_{T}, \beta_{T},}_{\text{home hours }} \underbrace{\alpha_{\delta}, \beta_{\delta}}_{\text{social norm}}\} \]
| Parmeter | Value | Target | Data | Model |
|---|---|---|---|---|
λR |
0.57 | mean of hf for regular workers |
0.50 | 0.48 |
λNR |
0.63 | mean of hf for NR workers |
0.30 | 0.27 |
θ |
2.96 | share of regular workers, females |
0.32 | 0.37 |
μNR |
−3.15 | share of NR workers, females |
0.38 | 0.28 |
σ |
1.03 | s.d. of ln wf) for R workers |
0.72 | 0.72 |
ρR, NR |
0.14 | mean diff. of ln wf, R and ln wf, NR |
0.62 | 0.62 |
ρmf |
0.01 | corr. of log wages, R×R couples |
0.49 | 0.50 |
γ |
0.84 | s.d. of hf for regular workers |
0.11 | 0.11 |
ξ |
−8.29 | s.d. of hf for NR workers |
0.14 | 0.15 |
αν |
13.04 | mean of Tm for regular workers |
0.14 | 0.13 |
βν |
1.15 | mean of Tm for NR workers |
0.13 | 0.14 |
αT |
1.59 | mean of Tf for regular workers |
0.28 | 0.21 |
βT |
3.57 | mean of Tf for NR workers |
0.32 | 0.37 |
αδ |
0.59 | share of couples with em < ef |
0.07 | 0.08 |
βδ |
11.81 | corr. of working hours, couples |
0.19 | 0.18 |
| Parmeter | Value | Target | Data | Model |
|---|---|---|---|---|
λR |
0.57 | mean of hf for regular workers |
0.50 | 0.48 |
λNR |
0.63 | mean of hf for NR workers |
0.30 | 0.27 |
θ |
2.96 | share of regular workers, females |
0.32 | 0.37 |
μNR |
−3.15 | share of NR workers, females |
0.38 | 0.28 |
σ |
1.03 | s.d. of ln wf) for R workers |
0.72 | 0.72 |
ρR, NR |
0.14 | mean diff. of ln wf, R and ln wf, NR |
0.62 | 0.62 |
ρmf |
0.01 | corr. of log wages, R×R couples |
0.49 | 0.50 |
γ |
0.84 | s.d. of hf for regular workers |
0.11 | 0.11 |
ξ |
−8.29 | s.d. of hf for NR workers |
0.14 | 0.15 |
αν |
13.04 | mean of Tm for regular workers |
0.14 | 0.13 |
βν |
1.15 | mean of Tm for NR workers |
0.13 | 0.14 |
αT |
1.59 | mean of Tf for regular workers |
0.28 | 0.21 |
βT |
3.57 | mean of Tf for NR workers |
0.32 | 0.37 |
αδ |
0.59 | share of couples with em < ef |
0.07 | 0.08 |
βδ |
11.81 | corr. of working hours, couples |
0.19 | 0.18 |
\(\xi < 0\)
| Parmeter | Value | Target | Data | Model |
|---|---|---|---|---|
λR |
0.57 | mean of hf for regular workers |
0.50 | 0.48 |
λNR |
0.63 | mean of hf for NR workers |
0.30 | 0.27 |
θ |
2.96 | share of regular workers, females |
0.32 | 0.37 |
μNR |
−3.15 | share of NR workers, females |
0.38 | 0.28 |
σ |
1.03 | s.d. of ln wf) for R workers |
0.72 | 0.72 |
ρR, NR |
0.14 | mean diff. of ln wf, R and ln wf, NR |
0.62 | 0.62 |
ρmf |
0.01 | corr. of log wages, R×R couples |
0.49 | 0.50 |
γ |
0.84 | s.d. of hf for regular workers |
0.11 | 0.11 |
ξ |
−8.29 | s.d. of hf for NR workers |
0.14 | 0.15 |
αν |
13.04 | mean of Tm for regular workers |
0.14 | 0.13 |
βν |
1.15 | mean of Tm for NR workers |
0.13 | 0.14 |
αT |
1.59 | mean of Tf for regular workers |
0.28 | 0.21 |
βT |
3.57 | mean of Tf for NR workers |
0.32 | 0.37 |
αδ |
0.59 | share of couples with em < ef |
0.07 | 0.08 |
βδ |
11.81 | corr. of working hours, couples |
0.19 | 0.18 |
\(\xi < 0\)
\(\alpha_{\nu} =\) 13.04, \(\beta_{\nu} =\) 1.15
| Parmeter | Value | Target | Data | Model |
|---|---|---|---|---|
λR |
0.57 | mean of hf for regular workers |
0.50 | 0.48 |
λNR |
0.63 | mean of hf for NR workers |
0.30 | 0.27 |
θ |
2.96 | share of regular workers, females |
0.32 | 0.37 |
μNR |
−3.15 | share of NR workers, females |
0.38 | 0.28 |
σ |
1.03 | s.d. of ln wf) for R workers |
0.72 | 0.72 |
ρR, NR |
0.14 | mean diff. of ln wf, R and ln wf, NR |
0.62 | 0.62 |
ρmf |
0.01 | corr. of log wages, R×R couples |
0.49 | 0.50 |
γ |
0.84 | s.d. of hf for regular workers |
0.11 | 0.11 |
ξ |
−8.29 | s.d. of hf for NR workers |
0.14 | 0.15 |
αν |
13.04 | mean of Tm for regular workers |
0.14 | 0.13 |
βν |
1.15 | mean of Tm for NR workers |
0.13 | 0.14 |
αT |
1.59 | mean of Tf for regular workers |
0.28 | 0.21 |
βT |
3.57 | mean of Tf for NR workers |
0.32 | 0.37 |
αδ |
0.59 | share of couples with em < ef |
0.07 | 0.08 |
βδ |
11.81 | corr. of working hours, couples |
0.19 | 0.18 |
\(\xi < 0\)
\(\alpha_{\nu} =\) 13.04, \(\beta_{\nu} =\) 1.15
\(\alpha_{T} =\) 1.59, \(\beta_{T} =\) 3.57
| Data | Model | Model / Data | Pct. | |
|---|---|---|---|---|
| Participation | 0.27 | 0.27 | 99% | |
| Occupation | 0.59 | 0.19 | 33% | |
| Labor Hours | 0.49 | 0.36 | 74% | |
| Wage | 0.76 | 0.26 | 34% |
| Data | Model | Model / Data | Pct. | |
|---|---|---|---|---|
| Participation | 0.27 | 0.27 | 99% | |
| Occupation | 0.59 | 0.19 | 33% | |
| Labor Hours | 0.49 | 0.36 | 74% | |
| Wage | 0.76 | 0.26 | 34% |
Model explains
| Data | Model | Model / Data | Pct. | |
|---|---|---|---|---|
| Participation | 0.27 | 0.27 | 99% | |
| Occupation | 0.59 | 0.19 | 33% | |
| Labor Hours | 0.49 | 0.36 | 74% | |
| Wage | 0.76 | 0.26 | 34% |
Model explains
Given a large amount of housework, women might not choose regular jobs
Social norms might lead wives to work less or not
To verify these arguments, I conduct experiments of \(\theta = 0\) and \(\delta = 0\)
Eliminating inflexibility encourages wives to have regular jobs
No social norms
\(\Rightarrow\) More wives choose regular job
\(\Rightarrow\) More husbands choose not to work
| Baseline | θ = 0.0 | δ = 0.0 | Gap θ | Gap δ | |
|---|---|---|---|---|---|
| Participation | 0.27 | 0.14 | −0.04 | ||
| Occupation | 0.19 | 0.01 | 0.18 | ||
| Labor Hours | 0.36 | 0.64 | 0.17 | ||
| Wage | 0.26 | −0.03 | 0.22 |
| Baseline | θ = 0.0 | δ = 0.0 | Gap θ | Gap δ | |
|---|---|---|---|---|---|
| Participation | 0.27 | 0.14 | −0.04 | ||
| Occupation | 0.19 | 0.01 | 0.18 | ||
| Labor Hours | 0.36 | 0.64 | 0.17 | ||
| Wage | 0.26 | −0.03 | 0.22 |
| Baseline | θ = 0.0 | δ = 0.0 | Gap θ | Gap δ | |
|---|---|---|---|---|---|
| Participation | 0.27 | 0.14 | −0.04 | ||
| Occupation | 0.19 | 0.01 | 0.18 | ||
| Labor Hours | 0.36 | 0.64 | 0.17 | ||
| Wage | 0.26 | −0.03 | 0.22 |
Outsourcing housework could increase women’s labor supply
Also discussed as the impact of low-skilled immigrants
However, those housework services are rarely used in Japan
\[\max_{h_m, h_f, j_m, j_f} U = \log c + \gamma \log H - \delta \mathbb{1}(e_m < e_f)\]
subject to
\[ \begin{aligned} c + pt &= e(h_m, j_m) + e(h_f, j_f)\\ H &= (\nu(1 - h_m - T_m)^\xi + (1 - \nu)(1 - h_f - T_f)^\xi)^{1/\xi} \\ T &= T_m + T_f + t \end{aligned} \]
\(t\): housework service
\(p\): price of housework service
Workers use outside services to do most of the home work
| Base | Outsourcing t | Gap remained | Pct. | |
|---|---|---|---|---|
| Participation | 0.27 | −0.02 | −7% | |
| Occupation | 0.19 | 0.03 | 15% | |
| Labor Hours | 0.36 | 0.06 | 17% | |
| Wage | 0.26 | 0.25 | 97% |
Given social norms, housework services
| Base | Outsourcing t | Gap remained | Pct. | |
|---|---|---|---|---|
| Participation | 0.27 | −0.02 | −7% | |
| Occupation | 0.19 | 0.03 | 15% | |
| Labor Hours | 0.36 | 0.06 | 17% | |
| Wage | 0.26 | 0.25 | 97% |
Given social norms, housework services
| Base | Outsourcing t | Gap remained | Pct. | |
|---|---|---|---|---|
| Participation | 0.27 | −0.02 | −7% | |
| Occupation | 0.19 | 0.03 | 15% | |
| Labor Hours | 0.36 | 0.06 | 17% | |
| Wage | 0.26 | 0.25 | 97% |
Given social norms, housework services
Erosa et al. (2022)
Cubas, Juhn, and Silos (2019)
Bertrand, Kamenica, and Pan (2015)
Kitao and Mikoshiba (2022)
To see the convex and linear wage schedules, similar to
Bick, Blandin, and Rogerson (2022),
\[y_{it} = a_{i} + \lambda_t + \left(\sum_{h \in H, h \ne 40} \beta_h I_{ith}\right) + \gamma X_{it} + \varepsilon_{it}\]
\(y_{it}\) : yearly earnings of individual \(i\) at time \(t\)
\(a_{i}\) : individual fixed effect
\(\lambda_{t}\) : time fixed effect
\(X_{it}\) : age, age-square, educational attainment, industry
\(H = \{20\mbox{-}24, 25\mbox{-}29, \dots, 60\mbox{-}64\}\) : 5 hour bins for weekly working hours
\(I_{ith}\) : indicator if \(i\)’s working hours in the bin \(h \in H\) at time \(t\)
Regular Jobs
Non-regular Jobs
Social Norms
Bertrand, Kamenica, and Pan (2015)
Japanese Data